We were in a similar, but less serious situation, so I looked into this some. I'll explain our situation and my understanding of things.
My wife has sole custody of my stepdaughter, but it does not preclude visitation rights. If your custody agreement bars all visitation, then you only need to show proof that all obligations under the custody agreement have been met. Otherwise, consent is required (I don't know about physically abusive relationships, and the possibility of legal documentation of this). In our case, rather than wade through the legal system in Cuba to change the custody agreement, it was easier to give the father a "gift" after signed the papers with a loose understanding of the content.
However, please take this with extreme caution, as our application hasn't been processed, and we did submit IMM5604.